This step-through was generated by Claude (Anthropic) for the DSP 101 course materials. Every product, every partial sum and every number on it is computed in your browser. The arithmetic line under panel 1 is not a summary of the calculation — the sample plotted in panel 2 is the sum of exactly the terms shown there. The four algebraic properties are evaluated by running the convolution both ways and differencing, never asserted. The spectra come from a real radix-2 FFT, and the agreement between X(k)·H(k) and Y(k) is measured and printed rather than claimed.

The room is a computed model, and no room was recorded. Its impulse response comes from the image-source method — mirroring the source in each of the six walls and summing the arrivals — which is the same mirror-image geometry the wireless propagation demo uses, in three dimensions. It is far sparser than a real room's response, because it follows only a few bounces per axis and models no diffusion. No measured reverberation time is offered: one was written and removed, because on a response this sparse the number came out 10–30× too short and moved in the wrong direction. The Sabine estimate beside the knobs is computed from the geometry and labelled as the model figure it is.

Every relation on this page is a definition or a theorem the course itself states — the convolution sum, the length law, the three algebraic properties, the impulse identity, and the convolution theorem with its transform-length condition. Nothing here rests on a figure transcribed from a standards document, so unlike the wireless demos this page raises no “verify against the source” flag. Room acoustics: Sabine's reverberation formula; the image-source method for a rectangular enclosure.

Chosen rather than computed, and marked where it matters: the preset sequences and their sample values, the default room dimensions and absorption, the reflection order the room model stops at, the level the response is normalised to, and the point at which the exponential (“IIR”) preset is truncated. That truncation is stated on the page rather than hidden: a genuinely infinite impulse response cannot be an array, and pretending otherwise would teach the error Lesson 3.4 exists to prevent.